A body with mass of 250 g is attached to the end of a spring that is stretched 25 cm by a force of 9 N. At time t=0 the body is pulled 1 m to the left. stretching the spring, and set in motion with an initial velocity of 5 m/s to the right. (a) Find x(t) in the form C cos (-a). (b) Find the amplitude and the period of motion of the body.

A ball whose mass is 1.4 kg is suspended from a spring whose stiffness is 40N/m. The ball oscillates up and down with an amplitude of 14 cm.  Suppose this apparatus were taken to the Moon, where the strength of the gravitational field is only 1/6 of that on Earth. What would be the period on the Moon? (Consider carefully how the period depends on properties of the system; look at the equation.)

Problem 9: An ideal pendulum of length L=1.1 m supports a mass of m =0.5 kg. Initially the pendulum is lifted such that it makes an angle of 0 = 26 degrees with respect to the vertical. m 10

(B) llllllll Students set up an experiment by attaching an ideal vertical spring to a support and hanging a block of known mass from the spring. The students pull the block down and release it from rest. The students then measure the period of the block's oscillation. This procedure is repeated for several trials using the same spring but with blocks of different known masses. The students are instructed to create a linear graph using the mass m of each block and the period T of the block's motion. The slope of the graph will be used to calculate the force constant k of the spring. Which of the following best indicates how the students should create their linear graph and how k can be calculated from the slope of the graph? E k Graph T on the vertical axis and m on the horizontal axis; set k = 2π slope Graph T² on the vertical axis and m on the horizontal axis; set k Graph T on the vertical axis and m² on the horizontal axis; set k Graph T² on the vertical axis and m on the horizontal…

A small steel ball is hanging by a light thread from the ceiling. The steel ball is then displaced 5.0 cm and makes 32 oscillations in exactly 50 s. Determine the period, T, angular frequency, w, and then write the motion of the steel ball as a function of time, t.

A mass-spring-dashpot system is modeled by the differential equation: x" + 4x + 5x = f(t) (a) What is the type of oscillatory motion of the mass? Explain. (b) Find the transient solution of the system. (c) Find the steady state solution of the system for f(t) = 4 cos wt for w= 1. Write your solution as C cos (wt -a). (d) Solve the initial value problem for z(0) = 12, x'(0) = 0. (e) Draw the steady state solution and describe the oscillation.

Consider a mass of 50kg attached to a spring to spring of 1800N/m and placed on a rough surface. The mass is subjected to a force F = 120cos(3t). Find the magnitude of the coefficient of friction if the maximum amplitude is not to exceed 75mm. Hint: μ ≤ 0.104 ww K →F(t) -ha

Hrlp

(a) A 40 g object hangs from a spring with spring constant 2 N/m, and oscillates with a frequency of 1.12 Hz and an amplitude of 8 cm. (i) If the mass is doubled to 80 g, what would the new frequency be?(ii) If the spring constant is doubled to 4 N/m, what would the new frequency be? (iii) If the amplitude is doubled to 16 cm, what would the new frequency be?

In order to study the long-term effects of weightlessness, astronauts in space must be weighed (or at least "massed). One way in which this is done is to seat them in a chair of known mass attached to a spring of known force constant and measure the period of the oscillations of this system. The 36.4-kg chair alone oscillates with a period of 1.25 s, and the period with the astronaut sitting in the chair is 2.24 s. Part A Find the force constant of the spring Express your answer in newtons per meter. k= N/m Submit Request Answer • Part B Find the mass of the astronaut. Express your answer in kilograms. kg